Finite Group Databasebeta

← C29×#9245 #20304145

Subgroups — C29×#9245 #20304145

Order 7424.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#478C211yesmaximal, characteristic
2C29×#2974C211yesmaximal, characteristic
3C29×#1528C211yesmaximal, characteristic, complemented
4C29×#1490C211yesmaximal, characteristic
5C29×#1470C211yesmaximal, characteristic, complemented
6C29×#1290C211yesmaximal, characteristic, complemented
7C29×#1283C211yesmaximal, characteristic, complemented
8C2×C29×#125C2211yescharacteristic
9C2×C4×D4×C29C2211yescharacteristic
10C29×#478—21no—
11C29×#478—21no—
12C29×#478—21no—
13C29×#478—21no—
14C29×#436—21no—
15C29×#435—22no—
16C8×D4×C29—21no—
17C29×#432C2211yescharacteristic
18C29×#432C2211yescharacteristic
19C29×#431C2211yescharacteristic
20C2×C29×#107C411yescharacteristic
21C2×C29×#106C411yescharacteristic
22C2×C29×C4⋊C8C2211yescharacteristic
23C2×C29×#102C411yescharacteristic
24C2×C29×#102C411yescharacteristic
25C29×#407—21no—
26C2×C29×C22⋊C8—21no—
27C4×M16×C29C2211yescharacteristic
28C29×#330—22no—
29C29×D4⋊C8—21no—
30C29×D4⋊C8—21no—
31C29×#324—21no—
32C29×#324—21no—
33C22×D4×C29C2×C411yescharacteristic
34C23×C4×C29—21no—
35C2×M16×C29—22no—
36C2×M16×C29—21no—
37C22×C8×C29—22no—
38C22×C8×C29C2×C411yescharacteristic
39C22×C8×C29C2×C411yescharacteristic
40C29×#125—21no—
41C29×#125—21no—
42C29×#125—21no—
43C29×#125—21no—
44C4×D4×C29—21no—
45C4×D4×C29—21no—
46C4×D4×C29D411yescharacteristic
47C4×D4×C29D411yescharacteristic
48C4×D4×C29D411yescharacteristic
49C4×D4×C29D411yescharacteristic
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29C2×C411yescharacteristic
53C2×C4⋊C4×C29C2×C411yescharacteristic
54C2×C4⋊C4×C29C2×C411yescharacteristic
55C2×C22⋊C4×C29—21no—
56C2×C42×C29C2311yescharacteristic
57C29×#107—21no—
58C29×#107—21no—
59C29×#106—21no—
60C29×#106—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×#102—21no—
67C29×#102—21no—
68C29×#102—21no—
69C29×#102—21no—
70C29×C22⋊C8—22no—
71C29×C22⋊C8—22no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8D411yescharacteristic
75C29×C22⋊C8D411yescharacteristic
76C29×#97—21no—
77C29×#97—21no—
78C29×#97D412yes—
79C4×C8×C29—21no—
80C4×C8×C29—21no—
81C24×C29—21no—
82C2×D4×C29—22no—
83C2×D4×C29—21no—
84C2×D4×C29—41no—
85C2×D4×C29C22⋊C411yescharacteristic
86C2×D4×C29C22⋊C411yescharacteristic
87C22×C4×C29—21no—
88C22×C4×C29—21no—
89C22×C4×C29—21no—
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29—82no—
95C22×C4×C29C22×C411yescharacteristic
96C22×C4×C29C2×D411yescharacteristic
97C22×C4×C29#4111yescharacteristic
98M16×C29—22no—
99M16×C29—41no—
100M16×C29—82no—
101C2×C8×C29—21no—
102C2×C8×C29—21no—
103C2×C8×C29—21no—
104C2×C8×C29—22no—
105C2×C8×C29—21no—
106C2×C8×C29—41no—
107C2×C8×C29—41no—
108C2×C8×C29—41no—
109C2×C8×C29—41no—
110C2×C8×C29—82no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—41no—
117C4⋊C4×C29—41no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—41no—
120C4⋊C4×C29C22⋊C411yescharacteristic
121C4⋊C4×C29C22⋊C411yescharacteristic
122C22⋊C4×C29—21no—
123C22⋊C4×C29—21no—
124C22⋊C4×C29—21no—
125C22⋊C4×C29—21no—
126C42×C29C2×D411yescharacteristic
127C42×C29C2×D411yescharacteristic
128C42×C29C2×D411yescharacteristic
129C42×C29#4111yescharacteristic
130#9245C2911yesmaximal, characteristic, direct product factor, Sylow
131C23×C29—21no—
132C23×C29—21no—
133C23×C29—42no—
134C23×C29—41no—
135C23×C29—41no—
136C23×C29—81no—
137C23×C29C4×D411yescharacteristic
138D4×C29—21no—
139D4×C29—21no—
140D4×C29—21no—
141D4×C29—42no—
142D4×C29#10112yes—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—41no—
150C2×C4×C29—42no—
151C2×C4×C29—42no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—41no—
155C2×C4×C29—41no—
156C2×C4×C29—81no—
157C2×C4×C29—81no—
158C2×C4×C29—81no—
159C2×C4×C29—81no—
160C2×C4×C29C2×C22⋊C411yescharacteristic
161C2×C4×C29C4×D411yescharacteristic
162C2×C4×C29#12011yescharacteristic
163C2×C4×C29#12111yescharacteristic
164C2×C4×C29#12111yescharacteristic
165C2×C4×C29#12311yescharacteristic
166C8×C29—41no—
167C8×C29—42no—
168C8×C29—41no—
169C8×C29—42no—
170C8×C29—41no—
171C8×C29—41no—
172C8×C29—81no—
173C2×#478C2×C2911yescharacteristic
174#2974C2×C2911yescharacteristic
175#1528C2×C2911yescharacteristic, complemented
176#1490C2×C2911yescharacteristic
177#1470C2×C2911yescharacteristic, complemented
178#1290C2×C2911yescharacteristic, complemented
179#1283C2×C2911yescharacteristic, complemented
180C22×C29—21no—
181C22×C29—21no—
182C22×C29—22no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29—82no—
189C22×C29—82no—
190C22×C29#38611yescharacteristic
191C22×C29#44311yescharacteristic
192C22×C29#44411yescharacteristic
193C4×C29—21no—
194C4×C29—21no—
195C4×C29—21no—
196C4×C29—21no—
197C4×C29—21no—
198C4×C29—41no—
199C4×C29—41no—
200C4×C29—81no—
201C4×C29—81no—
202C4×C29C2×#10111yescharacteristic
203C4×C29#41311yescharacteristic
204C2×#125C22×C2911yescharacteristic
205C2×C4×D4C22×C2911yescharacteristic
206#478—21no—
207#478—21no—
208#478—21no—
209#478—21no—
210#436—21no—
211#435—22no—
212C8×D4—21no—
213#432C22×C2911yescharacteristic
214#432C22×C2911yescharacteristic
215#431C22×C2911yescharacteristic
216C2×#107C4×C2911yescharacteristic
217C2×#106C4×C2911yescharacteristic
218C2×C4⋊C8C22×C2911yescharacteristic
219C2×#102C4×C2911yescharacteristic
220C2×#102C4×C2911yescharacteristic
221#407—21no—
222C2×C22⋊C8—21no—
223C4×M16C22×C2911yescharacteristic
224#330—22no—
225D4⋊C8—21no—
226D4⋊C8—21no—
227#324—21no—
228#324—21no—
229C2×C29—21no—
230C2×C29—21no—
231C2×C29—42no—
232C2×C29—81no—
233C2×C29#187611yescharacteristic
234C2×C29#190111yescharacteristic
235C2×C29#190411yescharacteristic
236C22×D4C2×C4×C2911yescharacteristic
237C23×C4—21no—
238C2×M16—22no—
239C2×M16—21no—
240C22×C8—22no—
241C22×C8C2×C4×C2911yescharacteristic
242C22×C8C2×C4×C2911yescharacteristic
243#125—21no—
244#125—21no—
245#125—21no—
246#125—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4D4×C2911yescharacteristic
250C4×D4D4×C2911yescharacteristic
251C4×D4D4×C2911yescharacteristic
252C4×D4D4×C2911yescharacteristic
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4C2×C4×C2911yescharacteristic
256C2×C4⋊C4C2×C4×C2911yescharacteristic
257C2×C4⋊C4C2×C4×C2911yescharacteristic
258C2×C22⋊C4—21no—
259C2×C42C23×C2911yescharacteristic
260#107—21no—
261#107—21no—
262#106—21no—
263#106—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269#102—21no—
270#102—21no—
271#102—21no—
272#102—21no—
273C22⋊C8—22no—
274C22⋊C8—22no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8D4×C2911yescharacteristic
278C22⋊C8D4×C2911yescharacteristic
279#97—21no—
280#97—21no—
281#97D4×C2912yes—
282C4×C8—21no—
283C4×C8—21no—
284C29#924511yescharacteristic, direct product factor, Sylow
285C24—21no—
286C2×D4—22no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4C22⋊C4×C2911yescharacteristic
290C2×D4C22⋊C4×C2911yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—82no—
299C22×C4C22×C4×C2911yescharacteristic
300C22×C4C2×D4×C2911yescharacteristic
301C22×C4#41×C2911yescharacteristic
302M16—22no—
303M16—41no—
304M16—82no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—82no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4C22⋊C4×C2911yescharacteristic
325C4⋊C4C22⋊C4×C2911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C42C2×D4×C2911yescharacteristic
331C42C2×D4×C2911yescharacteristic
332C42C2×D4×C2911yescharacteristic
333C42#41×C2911yescharacteristic
334C23—21no—
335C23—21no—
336C23—42no—
337C23—41no—
338C23—41no—
339C23—81no—
340C23C4×D4×C2911yescharacteristic
341D4—21no—
342D4—21no—
343D4—21no—
344D4—42no—
345D4C29×#10112yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4C2×C22⋊C4×C2911yescharacteristic
364C2×C4C4×D4×C2911yescharacteristic
365C2×C4C29×#12011yescharacteristic
366C2×C4C29×#12111yescharacteristic
367C2×C4C29×#12111yescharacteristic
368C2×C4C29×#12311yescharacteristic
369C8—41no—
370C8—42no—
371C8—41no—
372C8—42no—
373C8—41no—
374C8—41no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—82no—
385C22—82no—
386C22C29×#38611yescharacteristic
387C22C29×#44311yescharacteristic
388C22C29×#44411yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—81no—
397C4—81no—
398C4C2×C29×#10111yescharacteristic
399C4C29×#41311yescharacteristic
400C2—21no—
401C2—21no—
402C2—42no—
403C2—81no—
404C2C29×#187611yescharacteristic
405C2C29×#190111yescharacteristic
406C2C29×#190411yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C29×#1528C2semidirect
5. C29×#1470C2semidirect
6. C29×#1290C2semidirect
7. C29×#1283C2semidirect
130. #9245C29direct (N × H)
175. #1528C2×C29semidirect
177. #1470C2×C29semidirect
178. #1290C2×C29semidirect
179. #1283C2×C29semidirect
284. C29#9245direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C29×#4782
C29×#29742
C29×#15282
C29×#14902
C29×#14702
C29×#12902
C29×#12832
#924529